76 votes

Why aren't the energy levels of the Earth quantized?

The orbital energy of the Earth around the Sun is quantized. Measuring this quantization directly is infeasible, as I'll show below, but other experiments with bouncing neutrons (Nature paper) show ...
Mark H's user avatar
  • 24k
42 votes

What is the "secret " behind canonical quantization?

Indeed, canonical quantization works just when it works. It is in my view wrong and dangerous to think that this is the way to construct quantum theories even if it sometimes works: it produced ...
Valter Moretti's user avatar
20 votes
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First quantization vs second quantization

It is very complicated to construct a consistent quantum theory from scratch. One of the most general methods to do so is to take a classical theory, and imitate some of its ingredients - the most ...
AccidentalFourierTransform's user avatar
18 votes
Accepted

Name of concept: Replace classical variables by quantum operators

Canonical quantisation was introduced by Dirac in 1926
Charles Francis's user avatar
17 votes

Name of concept: Replace classical variables by quantum operators

Canonical quantization mentioned by @CharlesFrancis is probably the most precise answer. Colloquially one would often use term correspondence principle, also known as Bohr's correspondence principle, ...
Roger V.'s user avatar
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16 votes
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Why do negative norm states break unitarity?

I asked Mark Srednicki about this, and he told me that it's not really correct to say that negative-norm states break unitarity, because negative-norm states don't exist by the definition of the inner ...
tparker's user avatar
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16 votes
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Why there is no unique "recipe" for quantization of a classical theory?

Reverse the burden: Why should there be a unique quantization method? The classical theory is a limit of the quantum theory, why should this limit be reversible? It's like asking thermodynamics to be ...
ACuriousMind's user avatar
  • 124k
14 votes

Is this four-step recipe for quantization always valid?

Suppose your classical hamiltonian is $H(x,p) = x^2 p^2$. What quantum hamiltonian operator will your recipe produce? You might say it's $\hat{H} = \hat{x}^2 \hat{p}^2$. However classically $x$ and $p$...
d_b's user avatar
  • 8,086
13 votes
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Gupta-Bleuler and Lorenz Gauge: I don't understand the principle behind Gupta-Bleuler

The sketch of the philosophy: You modified the Lagrangian by introducing the $\xi$ term. This shouldn't really bother you because the Lagrangian is not measurable, so there is, in principle, nothing ...
AccidentalFourierTransform's user avatar
13 votes

Why aren't the energy levels of the Earth quantized?

They are. It is just that they are so closely spaced between each other that we can't observe it. Note that we do not yet have a good theory of quantum gravity.
Ivan Burbano's user avatar
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13 votes
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What do we mean by radial quantisation in CFT?

The starting point is to consider a CFT on a sphere, $S^{d-1}$ so the manifold under consideration is the "cylinder" $S^{d-1} \times {\mathbb R}$ with metric $$ ds^2 =- dt^2 + R^2 d\Omega_{d-1}^2 $$ ...
Prahar's user avatar
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11 votes
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$\pi$, $\sigma$ - atomic transitions with respect to the magnetic field axis

a: In case 4, what kind of transition will happen? In this case, the radiation can excite both $\sigma$ and $\pi$ transitions, although you wouldn't really call them that. More specifically, it can ...
Emilio Pisanty's user avatar
10 votes

In quantum mechanics, how exactly do we associate Hermitian operators to classical observables?

There doesn't exist any procedure to uniquely associate a Hermitian operator $L$ to a function of the phase space $f(x,p)$. Quantum mechanics is a theory that exists independently of classical physics....
Luboš Motl's user avatar
10 votes

Why aren't the energy levels of the Earth quantized?

tl;dr- In principle, quantization might still apply. Scientifically speaking, we have no idea yet. We don't know how far down our current quantum theories might hold. To draw an analogy, Newton's ...
Nat's user avatar
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10 votes
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What is the rigorous definition of the verb "to quantize"?

There are quite a number of notions of quantisation. It is a theorem by van Hove & Groenewald that the naive notion of quantisation that is usually taught where position and momentum are mapped to ...
Mozibur Ullah's user avatar
9 votes
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What are the minimal postulates to do quantum mechanics in path-integral formulation without knowing the operator formulation?

The path integral formalism doesn't really replace the operator formalism. You still need to know that the state space is a Hilbert space, that probabilities are computed by norm-squaring inner ...
user1504's user avatar
  • 16.3k
8 votes

Derivative interaction: $\mathcal{H}_\mathrm{int}\neq - \mathcal{L}_\mathrm{int}$. Question about Feynman Rules

Some general remarks: In the operator formalism, the non-covariant extra term in the Hamiltonian is cancelled by a non-covariant term coming from the naïve time ordering symbol: $$ \mathrm T\sim\...
AccidentalFourierTransform's user avatar
8 votes
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What is "quantization"? Give one example

Before quantum theory we had classical theories. There was no notion of energy in particles being stores in "a lump". Instead classical theories (in general) allow energy to be split up into ...
StephenG - Help Ukraine's user avatar
8 votes

What is the "secret " behind canonical quantization?

Instead, we were given a recipe how to quantize a classical theory, which is based on the rule of transforming all quantities to operators, and that Poisson bracket is transformed to a commutator. For ...
Cosmas Zachos's user avatar
8 votes
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Why are first class constraints harder to quantize than second class constraints?

First-class constraints generate gauge transformations (assuming the Dirac conjecture), i.e. map physically equivalent states onto each other. Even if you do not assume the Dirac conjecture, then ...
ACuriousMind's user avatar
  • 124k
7 votes

Difference between discretization and quantization in physics

Forget about language issues for a moment. The crucial feature of quantum mechanics is quantum-mechanical interference of probability amplitudes, which most people understand as a wave phenomenon (but ...
Cosmas Zachos's user avatar
7 votes

The most general procedure for quantization

Here are some comments on the literature, maybe serving to put Valter Moretti's more concrete response into a broader perspective. The question asked is a surprisingly good question. It is "good", ...
Urs Schreiber's user avatar
7 votes
Accepted

What has "quantisation" to do with associated graded algebras?

The mathematical term of "quantization" of algebras is much broader than the physical notion of quantization of a classical theory, however, a very prominent quantization in the mathematical sense ...
ACuriousMind's user avatar
  • 124k
7 votes
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Physically distinct quantizations

But...did you specify the problem? Which problem? Of course you have physically distinct predictions. Which ones do you want to use and where? Crehan's paper finds all 2-parameter (ħ,α) deformations ...
Cosmas Zachos's user avatar
7 votes
Accepted

Is it possible to combine two photons of different energies to get a single photon of a higher (combined) energy?

To answer the question in the title, yes, see this link. It is also possible to combine more photons in order to get superior harmonics. For this you have a list that you can use to get some fast info ...
Victor Palea's user avatar
7 votes
Accepted

(Anti)commutation of ghosts and fermions

It is not completely clear what OP is looking for, but here are some hopefully helpful comments: Classically (meaning when Planck constant $\hbar\to 0$), two fields $A$ and $B$ are super-commutative ...
Qmechanic's user avatar
  • 200k
7 votes

Is this four-step recipe for quantization always valid?

No. There remains an ambiguity of ordering. See for instance this post for an example where there could be different outcomes of quantization depending on the ordering, and where your 4-step approach ...
ZeroTheHero's user avatar
  • 45.4k
6 votes

Can one quantize systems with local (non-gauge!) symmetries?

Why local transformations must be gauge transformations: Traditionally, quantization is recipe in which the phase space of a classical system is replaced by a Hilbert space of a quantum system; and ...
David Bar Moshe's user avatar
6 votes

Why does a photon have to be one wavelength?

To put things plainly: photons do not have to have a well-defined wavelength. The states of the field which have a single photon present (i.e. states with well-defined photon number equal to one) and ...
Emilio Pisanty's user avatar
6 votes
Accepted

Uniqueness in the path integral vs canonical quantisation

In quantum mechanics it is well known that if you have a Lagrangian L and you want to quantise it, there is no unique way of doing this. This is correct, however note that you also have the ...
lakehal's user avatar
  • 618

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